In this paper, the nonuniqueness of BIEM and BEM are studied by using SVD technique. It contains the nonuniqueness solution for degenerate boundary, degenerate scale, spurious eigenvalue and fictitious frequency. First, the influence matrices in the dual BIEM and dual BEM are constructed. Mathematically speaking, it stems from the rank deficiency of influence matrices. After employing the SVD technique with respect to the four influence matrices, it is found that true (physics) information is imbedded in the right unitary matrix while the spurious or fictitious (numerics) information appears in the left hand side. Several approaches, hypersingular formulation, SVD updating term and updating document technique, complex-valued formulation, CHIEF and CHEEF concept, were applied to ensure the unique solution. Four simple examples are demonstrated to see the validity of the present formulation.